Theorems · Theorem · measure theory
MeasureTheory.toMeasure_apply
∀ {α : Type u_1} [ms : MeasurableSpace α] (m : MeasureTheory.OuterMeasure α) (h : ms ≤ m.caratheodory) {s : Set α},
MeasurableSet s → (m.toMeasure h) s = m s- Cited by
- 10 results in Mathlib
- Foundations
- Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasurableSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement · cited by 10,939
- ENNRealstatement · cited by 9,879
- MeasurableSetstatement and proof · cited by 3,075
- MeasureTheory.OuterMeasurestatement and proof · cited by 287
- MeasureTheory.OuterMeasure.caratheodorystatement and proof · cited by 37
- MeasureTheory.OuterMeasure.toMeasurestatement · cited by 11
- MeasureTheory.OuterMeasure.trim_eqproof · cited by 8
Cited by10
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.sum_applyproof · cited by 50
- MeasureTheory.Measure.dirac_apply'proof · cited by 43
- MeasureTheory.trim_measurableSet_eqproof · cited by 22
- PMF.toMeasure_apply_eq_toOuterMeasure_applyproof · cited by 15
- MeasureTheory.Content.measure_applyproof · cited by 6
- MeasureTheory.OuterMeasure.toMeasure_zeroproof · cited by 3
- MeasureTheory.Measure.sInf_applyproof · cited by 2
- MeasureTheory.Measure.liftLinear_applyproof · cited by 2
- MeasureTheory.toMeasure_apply₀proof · cited by 2
- MeasureTheory.Measure.pi_pi_auxproof · cited by 1